The Schwarz Lemma at the Boundary of the Egg Domain Bp1,p2 in Cn
Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 381-392
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Let ${{B}_{p1,p2}}\,=\,\left\{ z\,\in \,{{\mathbb{C}}^{n}}\,:\,{{\left| {{z}_{1}} \right|}^{{{p}_{1}}}}\,+\,{{\left| {{z}_{2}} \right|}^{{{p}_{2}}}}\,+\,\cdots \,+\,{{\left| {{z}_{n}} \right|}^{{{p}_{2}}}}\,<\,1 \right\}$ be an egg domain in ${{\mathbb{C}}^{n}}$ . In this paper, we first characterize the Kobayashi metric on ${{B}_{{{p}_{1}},{{p}_{2}}}}\,\left( {{p}_{1}}\,\ge 1,\,{{p}_{2}}\,>\,1 \right)$ and then establish a new type of classical boundary Schwarz lemma at ${{z}_{0}}\in \partial {{B}_{{{p}_{1}},{{p}_{2}}}}$ for holomorphic self-mappings of ${{B}_{{{p}_{1}},{{p}_{2}}}}\,\left( {{p}_{1}}\,\ge \,1,\,{{p}_{2}}\,>\,1 \right)$ ), where ${{z}_{0}}={{\left( {{e}^{i\theta }},\,0,\ldots ,0 \right)}^{\prime }}$ and $\theta \,\in \,\mathbb{R}$ .
Mots-clés :
32H02, 30C80, 32A30, holomorphic mapping, Schwarz lemma, Kobayashi metric, egg domain
Tang, Xiaomin; Liu, Taishun. The Schwarz Lemma at the Boundary of the Egg Domain Bp1,p2 in Cn. Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 381-392. doi: 10.4153/CMB-2014-067-7
@article{10_4153_CMB_2014_067_7,
author = {Tang, Xiaomin and Liu, Taishun},
title = {The {Schwarz} {Lemma} at the {Boundary} of the {Egg} {Domain} {Bp1,p2} in {Cn}},
journal = {Canadian mathematical bulletin},
pages = {381--392},
year = {2015},
volume = {58},
number = {2},
doi = {10.4153/CMB-2014-067-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-067-7/}
}
TY - JOUR AU - Tang, Xiaomin AU - Liu, Taishun TI - The Schwarz Lemma at the Boundary of the Egg Domain Bp1,p2 in Cn JO - Canadian mathematical bulletin PY - 2015 SP - 381 EP - 392 VL - 58 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-067-7/ DO - 10.4153/CMB-2014-067-7 ID - 10_4153_CMB_2014_067_7 ER -
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